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化学进展 2012, Vol. 24 Issue (06): 910-927 前一篇   后一篇

• 量子化学专辑 •

带隙问题:第一性原理电子能带理论研究现状

蒋鸿*   

  1. 北京分子科学国家实验室稀土材料化学和应用国家重点实验室 理论与计算化学研究所 北京大学化学与分子工程学院 北京 100871
  • 收稿日期:2012-01-01 修回日期:2012-03-01 出版日期:2012-06-24 发布日期:2012-05-11
  • 通讯作者: 蒋鸿 E-mail:h.jiang@pku.edu.cn
  • 基金资助:

    国家自然科学基金面上资助项目(No.20973009,No.21173005)

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The Band Gap Problem: the State of the Art of First-Principles Electronic Band Structure Theory

Jiang Hong   

  1. Beijing National Laboratory of Molecular Sciences, State Key Laboratory of Rare Earth Materials Chemistry and Applications, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
  • Received:2012-01-01 Revised:2012-03-01 Online:2012-06-24 Published:2012-05-11
电子能带结构是材料最基本的性质之一,对于材料的实际应用具有深刻影响。电子能带结构的理论描述一直以来都是第一性原理理论方法中最具挑战性的问题之一。作为材料理论计算“标准模型”的密度泛函理论,在局域密度近似或广义梯度近似下,存在着著名的“带隙问题”:半导体材料的理论带隙与实验值相比存在着显著的系统性误差。近年来,以改进对带隙的描述为主要目标之一,密度泛函理论领域有很多重要发展。同时,对于带隙问题,与密度泛函理论紧密相关但又有本质区别的另外一类理论方法是基于格林函数的第一性原理多体微扰理论,其中最为流行的GW方法是当前描述材料的电子能带结构最为准确的第一性原理方法,但一直以来都受限于计算量太大而无法应用于更复杂的体系。本文综述了密度泛函理论和格林函数多体理论在电子能带结构问题上的基本原理、最新进展以及存在的挑战性问题。希望通过比较两种理论框架的异同,为未来可能的发展思路提供启发。
关键词： 电子能带结构, 带隙问题, 密度泛函理论, 广义Kohn-Sham, 格林函数, 多体微扰理论, GW近似
Electronic band structure is one of the most fundamental properties of a material that plays a crucial role in many important applications, and its accurate description has been a long-standing challenge for the first-principles electronic structure theory. Kohn-Sham Density-functional theory (KS-DFT) within local density or generalized-gradient approximations (LDA/GGA), currently the “standard model” for first-principles computational materials science, suffers from the well-known band gap problem. A lot of efforts have been invested to improve the description of band gaps within the framework of Kohn-Sham DFT or its generalized formalisms. On the other hand, many-body perturbation theory (MBPT) based on Green's function G (GF) provides a different and conceptually more rigorous framework for electronic band structure. The central ingredient of the GF-based MBPT is the exchange-correlation self-energy ∑xc, which can be formally obtained by solving a set of complicated integro-differential equations, named Hedin's equations. The GW approximation, in which ∑xc is simply a product of G and the screened Coulomb interaction (W), is currently the most accurate first-principles approach to describe electronic band properties of extended systems. Compared to LDA/GGA, the computational efforts required for GW calculations are much heavier, so that its applications have been limited to relatively small systems. In this work, we review the basic principles, latest developments, and remaining challenges of first-principles electronic band structure theory from both DFT and GF-based MBPT perspectives. It is hoped that new ideas on further developments can be obtained by setting up the connection between the two different theoretical frameworks. Contents
1 Introduction:Electronic band structures and the band gap problem
1.1 Experimental measurements of electronic band structures
1.2 Theoretical treatments of electronic band structures and the band gap problem
2 Electronic band structures frommean-field approaches
2.1 Hartree theory
2.2 Hartree-Fock theory
3 Electronic band structures from density functional theory
3.1 Density functional theory and Kohn-Sham equations
3.2 The band gap problem and its origin
3.3 The optimized effective potential and related methods
3.4 Generalized Kohn-Sham methods
4 Electronic band structures from Green's function based many-body perturbation theory
4.1 Green's function
4.2 Self-energy and quasi-particle equations
4.3 Hedin's equations and GW approximation
4.4 The G0W0 approach and self-consistency
5 Concluding remarks
Key words: electronic band structure, the band gap problem, density-functional theory, generalized Kohn-Sham, Green&rsquo, s function, many-body perturbation theory, GW approximation

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